if you say:" i will help you" , that means that you are trying to help him , you plan to help him or you are promissing him. but when you say:" let me help you" , that means that you ask that guy to allow yoiu help him, and that can mean that you love that person, or you think he is not able to do his tasks, or may be because he want to offer him some help.
"I will help you" means that you are telling the person you shall do something whether they like it or not.
"Let me help you" shows that the person speaking wants to help the person, but is allowing the other person to refuse that help. Number two is asking for the persons permission to help, in a way.